Linear transport through a quantum dot coupled to a topological nanowire

• Grant number: 22/14145-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: José Carlos Egues de Menezes
• Grantee: João Pedro Carvalho Costa
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This new project is a continuation of a successful previous PUB/USP ("Program Unificado de Bolsas USP") project that has been carried out by the undergraduate research student João Pedro; this project ended in Aug/2022. The student was granted another PUB/USP scholarship (since 09/2022), but we would like to apply for a FAPESP scholarship as it is more prestigious and also because João Pedro could benefit from the "reserva técnica". Of course, he would only keep one scholarship, should FAPESP grant him a new scholarship. The ongoing scholarship would possibly be transferred to another undergraduate research student in my group. As part of the documents in this application, we attach the scientific report describing the results João Pedro obtained within this earlier project (Sept/2021-Ago/2022). The student learned a great deal of (introductory) quantum mechanics (bound and scattering states), solid state physics, numerical diagonalization, etc. and not only carried out the originally proposed research plans but also obtained results beyond the initial plan. As his report shows, João Pedro was able to reproduce with analytical and numerical methods, results in the recent literature for the conductance of topological Kitaev wires coupled to metallic leads. The results he has reproduced were published by leading groups in the area (e.g., the group of Das Sarma in Maryland, see references at the end of João Pedro's report.) Here we present a project and a plan of work to explore in detail the parameter space of the topological nanowire, which has been previously studied and is currently being investigated by João Pedro, aiming at finding new physical phenomena. We should emphasize that what has been done so far - from the stand point of an undergraduate research project - is indeed remarkable. The amount of work and results generated are impressive (the report below from João Pedro's previous investigation presents only a summary of the findings). Also impressive is how the student was able to quickly learn to navigate through advanced topics in condensed matter theory - even if not grasping entirely the deep implications of what he was studying. This is what he is going to focus on in this new stage. This second year will basically serve two purposes: 1) to explore the parameter space of the system (realistically with an effective model - see plan of work in the text of the proposal) to try to find relevant new physical phenomena and 2) to gain a more physical understanding of the results already obtained and those to be generated. In 1) the basic idea is to explore the Kitaev model and its parent model, i.e., a nanowire with spin-orbit interaction, Zeeman field and proximity induced superconductivity, to obtain realistic estimates of parameters leading to novel physical phenomena (e.g., non-local conductance etc.). In 2) the student will describe in detail all the microscopic processes behind the features seen in the conductance plots. These correspond to the so-called Andreev processes. They are of several types: local and cross Andreev processes, direct and inverse Andreev processes, resonant Andreev process etc. It is not unconceivable that this project leads to the discovery of new physical phenomena that could potentially give rise to a publication in world-class scientific journals.